Quantum teleportation with infinite reference frame uncertainty and without prior alignment

TL;DR

This paper introduces two innovative quantum teleportation schemes that operate without prior reference frame alignment and are robust against reference frame drift, improving purity and achieving perfect teleportation under certain conditions.

Contribution

The paper presents two new schemes for quantum teleportation that do not require reference frame alignment and are resilient to reference frame changes during execution.

Findings

The tight scheme improves purity compared to standard teleportation.

The perfect scheme achieves flawless teleportation but conveys some reference frame information.

Both schemes are based on a unitary error basis permuted by a finite subgroup of G.

Abstract

We present two new schemes for quantum teleportation between parties whose local reference frames are misaligned by the action of a compact Lie group G. These schemes require no prior alignment of reference frames and are unaffected by arbitrary changes in reference frame alignment during execution, suiting them to situations of rapid reference frame drift. Our tight scheme yields improved purity compared to standard teleportation, in some cases substantially --- this includes the case of qubit teleportation under arbitrary SU(2) reference frame uncertainty--- while communicating no information about either party's reference frame alignment at any time. Our perfect scheme performs perfect teleportation, but does communicate some reference frame information. The mathematical foundation of these schemes is a unitary error basis permuted up to a phase by the conjugation action of a finite subgroup of G.